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Applying The Capital Asset Pricing Model Case Solution
The capital asset market is based on a number of assumptions that might not hold if the efficient markets hypothesis is violated. A lot of research has been conducted to show that factors such as company size, industry trends, economic state, and dividend policies affect the return generated by stocks. These anomalies seem to be arguing against that CAPM, which predicts that market movements should fully explain stock returns. The question is: how much role these anomalies play in dictating stock returns. Researchers use the term alpha to describe the abnormal return – return that is different from the expected return under CAPM – generate by assets or stocks. A lot of research has been conducted to determine if the alpha generated by stocks is significant enough to compromise the validity of CAPM.
Following questions are answered in this case study solution
Describe the CAPM model and present it as a regression model. Would you include an intercept in this model? Explain your answer.
Present and briefly comment on the economic evidence in the literature with regard to this model.
In the light of the above answer, how useful do you think reliance on the model is for an investor?
Case Analysis for Applying The Capital Asset Pricing Model
1. Describe the CAPM model and present it as a regression model. Would you include an intercept in this model? Explain your answer.
The Capital Asset Pricing model attempts to price various assets in accordance with their riskiness relative to an all-encompassing market portfolio. The underlying concept behind the CAPM is that investors can easily diversify their unique risks and are only systematic risk – the risk inherent in a market portfolio. Ideally, the market portfolio includes all types of observable assets including equities, fixed income securities, and physical assets. However, a more simplistic model usually takes a large stock index as a proxy for market portfolio. The reasoning behind the model is that an investor should not worry about the individual changes the stock returns (unique risk), but only about the changes in the stock returns that correlate with changes in market returns. This idea based on Harry Markowitz’s theory of portfolio diversification that forms the basis of modern portfolio management (Markowitz, 1952). While the model is based on a simple idea, it makes a number of assumptions before making any predictions (Defuso et al., 2004):
Investors are aware of the expected returns, variances, and covariance of all assets involved.
Investors have homogenous expectations about the variables involved.
Investors can easily buy, sell and short sell assets without any influence on price.
Investors can borrow and lend at the risk-free rate without any limitations.
Markets are frictionless – investors pay no taxes and/or transactions costs on trades.
If these assumptions hold, CAPM delineates that the following equation can be used to derive the expected return on any security:
E(Ri) = Rf + βi [E(Rm) – Rf]
E(Ri) = expected return on asset i
Rf = risk-free rate
βi = beta of asset i
E(Rm) = expected return on market portfolio
The mechanics behind the CAPM equation are exceedingly simple. The risk-free rate is the rate that an investor can obtain by investing in a riskless security. The treasury securities are often used as an example of a risk-free security since the securities are guaranteed by the federal government. The risk-free rate is the minimum rate an investor should be getting for investing in a security. However, many assets also embody a certain degree of risk such as default or liquidity risk. Therefore, many securities will offer a risk premium. The CAPM equation compensates for this risk premium with the component βi [E(Rm) – Rf], representing the asset’s risk premium. E(Rm) – Rf is the difference between return on market portfolio and the risk-free rate and represents the market risk premium. The beta (βi) is measure of asset return sensitivity to market returns. It is meant to scale the market risk premium into as asset-specific risk premium.
In econometrics, a popular way of using the CAPM model is the use the Sharpe-Litner version of the CAPM model. Under this model the risk-free rate from the standard CAPM is moved from right hand side of the equation to the left hand side so that the equation becomes:
E(Ri) - Rf = + βi [E(Rm) – Rf]
This equation can be restated in the following form:
Zi = βi Zm
Zi = E(Ri) - Rf
Zm= E(Rm) – Rf
Historical data about Zi and Zm can be used to form a regression equation, which takes the following form:
Zi = αi + βi Zm + ϵ
αi = intercept
ϵ = error term
The most important variable that can be obtained from this equation is the regression coefficient beta (βi). The beta represents the responsiveness on asset’s return to the returns of the market. This historical estimate of the beta can be used to forecast future returns on the asset i based on the future expected returns on the market. It is important to note that the intercept of the regression equation – αi – is expected to be zero in this regression equation. This is because the risk-free rate, which is estimated by the intercept in standard CAPM models, has already been accounted for in the dependant variable (Zi) of the regression equation. Therefore, it is not possible to use the intercept as a historical estimate of the risk-free rate when using this regression equation
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